Chapter 4 Calculus of Inductive Constructions 4.1 The terms 4.2 Typed terms 4.3 Conversion rules 4.4 Derived rules for environments 4.5 Inductive Definitions 4.6 Coinductive types 4.7 Cic: the Calculus of Inductive Construction with impredicative Set The underlying formal language of Coq is a Calculus of Constructions with Inductive Definitions. It is presented in this chapter. For Coq ver